This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews.

The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. (The Cantor-Bernstein-Schröeder theorem has been added.) The two editions can be used interchangeably, except for the last few pages of Chapter 13. (But you can download them here.)

Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. Click here for a pdf copy of the entire book, or get the chapters individually below.Note to adopters: Your bookstore will need to know that the book is distributed by Ingram. Please let me know if you use this book in your classes. I maintain a list of known adoptions here. Thanks!

Thanks to readers around the world who wrote to report mistakes and typos! I will continue to incorporate reader feedback in periodic revisions. Please contact me if you find any additional mistakes. My email address is on my home page.

Instructors: Click here for my page for VCU's MATH 300, a course based on this book. The page has a syllabus, calendar, sample tests, etc.

I will always offer the book for free on my web page, and for the lowest possible price through on-demand publishing.